Center for Agricultural Water Research in China, College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China.
Int J Environ Res Public Health. 2019 May 28;16(11):1884. doi: 10.3390/ijerph16111884.
In this study, a nonlinear inexact two-stage management (NITM) model is proposed for optimal agricultural irrigation water management problems under uncertainty conditions. The model is derived from incorporating interval parameter programming (IPP), two-stage stochastic programming (TSP) and quadratic programming (QP) within the agricultural water management model. This model simultaneously handles uncertainties not only in discrete intervals, but also in probability distributions, as well as nonlinearity in the objective function. A concept of the law of diminishing marginal utility is introduced to reflect the relationship between unit benefits and allocated water, which can overcome the limitation of general TSP framework with a linear objective function. Moreover, these inexact linear functions of allocated water can be obtained by an interval regression analysis method. The model is applied to a real-world case study for optimal irrigation water allocation in midstream area of the Heihe River Basin in northwest China. Two Heihe River ecological water diversion plans, i.e. the original plan and an improved plan, will be used to determine the surface water availabilities under different inflow levels. Four scenarios associated with different irrigation target settings are examined. The results show that the entire study system can arrive at a minimum marginal utility and obtain maximum system benefits when optimal irrigation water allocations are the deterministic values. Under the same inflow level, the improved plan leads to a lower water shortage level than that of the original plan, and thus leads to less system-failure risk level. Moreover, the growth rate of the upper bound of economic benefits between each of two scenarios based on the improved plan are greater than that from the original plan. Therefore, these obtained solutions can provide the basis of decision-making for agricultural water allocation under uncertainty.
本研究提出了一种用于不确定性条件下最优农业灌溉水资源管理问题的非线性不精确两阶段管理（NITM）模型。该模型通过将区间参数规划（IPP）、两阶段随机规划（TSP）和二次规划（QP）纳入农业水资源管理模型中而得到。该模型同时处理不仅离散区间而且概率分布中的不确定性，以及目标函数中的非线性。引入边际效用递减规律的概念来反映单位效益与分配水量之间的关系，从而克服了具有线性目标函数的一般 TSP 框架的局限性。此外，可以通过区间回归分析方法获得分配水量的这些不精确线性函数。该模型应用于中国西北黑河流域中游地区的最优灌溉水资源分配的实际案例研究。将使用两个黑河生态调水方案，即原方案和改进方案，来确定不同来水水平下的地表水可利用量。考察了与不同灌溉目标设置相关的四个情景。结果表明，当最优灌溉水资源分配为确定性值时，整个研究系统可以达到最小边际效用并获得最大系统效益。在相同的来水水平下，改进后的方案导致的缺水水平低于原始方案，从而导致的系统失效风险水平较低。此外，基于改进方案的两个方案中每个方案的经济利益上限的增长率都大于原始方案。因此，这些获得的解决方案可以为不确定性下的农业水资源分配提供决策依据。
